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 A043547 Odd numbers interspersed with double the previous odd number. 10
 1, 2, 3, 6, 5, 10, 7, 14, 9, 18, 11, 22, 13, 26, 15, 30, 17, 34, 19, 38, 21, 42, 23, 46, 25, 50, 27, 54, 29, 58, 31, 62, 33, 66, 35, 70, 37, 74, 39, 78, 41, 82, 43, 86, 45, 90, 47, 94, 49, 98, 51, 102, 53, 106, 55, 110, 57, 114, 59, 118, 61, 122, 63, 126, 65, 130, 67, 134 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As pointed out by E. Angelini on the SeqFan list (cf. link), this is the lexicographically earliest sequence of positive integers without repetitions such that the sum of four consecutive terms is always a multiple of 4. - M. F. Hasler, Mar 22 2013 LINKS Table of n, a(n) for n=1..68. E. Angelini, k-chunks sum and division by k, post to the SeqFan list, Mar 22 2013 Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA a(n) = (2 - n) * (n - floor(n/2) * 2) + 2 * (n - 1). G.f.: x*(1+2*x)*(1+x^2)/(1-x^2)^2. - Ralf Stephan, Jun 10 2003 a(2n-1) = 2n-1, a(2n) = 4n-2. - M. F. Hasler, Mar 22 2013 From Wesley Ivan Hurt, Nov 22 2015: (Start) a(n) = 2*a(n-2) - a(n-4) for n>4. a(n) = n*(-1)^n/2 - (-1)^n + 3*n/2 - 1. (End) EXAMPLE a(1)=1 because n is odd. a(2)=2 because a(1)*2=2. MAPLE A043547:=n->n*(-1)^n/2-(-1)^n+3*n/2-1: seq(A043547(n), n=1..100); # Wesley Ivan Hurt, Nov 22 2015 MATHEMATICA Flatten[Table[Accumulate[{2 n - 1, 2 n - 1}], {n, 40}]] (* Wesley Ivan Hurt, Nov 22 2015 *) With[{o=Range[1, 71, 2]}, Riffle[o, 2o]] (* Harvey P. Dale, Sep 17 2019 *) PROG (PARI) A043547(n)=n+!bittest(n, 0)*(n-2) \\ M. F. Hasler, Mar 22 2013 (Magma) [n*(-1)^n/2-(-1)^n+3*n/2-1 : n in [1..50]]; // Wesley Ivan Hurt, Nov 22 2015 (PARI) Vec(x*(1+2*x)*(1+x^2)/(1-x^2)^2 + O(x^100)) \\ Altug Alkan, Nov 22 2015 CROSSREFS For n>3, a(n) = A059029(n-3)+3. For n>1, a(n) = A022998(n-2)+2. Sequence in context: A091239 A145110 A257405 * A338702 A064919 A064923 Adjacent sequences: A043544 A043545 A043546 * A043548 A043549 A043550 KEYWORD easy,nonn AUTHOR Jim Cook (jcook(AT)halcyon.com), Mar 01 2000 EXTENSIONS More terms from James A. Sellers, Mar 01 2000 STATUS approved

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Last modified February 29 17:30 EST 2024. Contains 370428 sequences. (Running on oeis4.)